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A projectile is given an initial velocity of $(i^+2j^ )m/s,$ where $i^$ is along the ground and $j^ $ is along the vertical. If $g=10m/s_{2},$ the equation of its trajectory is:

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The number of common tangents to the circles $x_{2}+y_{2}-4x-6y-12=0$ and $x_{2}+y_{2}+6x+18y+26=0$, is :

Let f(x) be a polynomial of degree four having extreme values at $x=1$and $x=2$. If $(lim)_{x0}[1+x_{2}f(x) ]=3$, then f(2) is equal to :

The locus of the foot of perpendicular drawn from the centre of the ellipse $x_{2}+3y_{2}=6$on any tangent to it is

The sum of coefficients of integral powers of x in the binomial expansion of $(1−2x )_{50}$ is:

A compound with molecular mass 180 is acylated with $CH_{3}COCl$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n - 1). If $n>>1,$ the frequency of radiation emitted is proportional to

If a piece of metal is heated to temperature $θ$ and then allowed to cool in a room which is at temperature $θ_{0}$ the graph between the temperature T of the metal and time t will be closest to :

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $σ$ at equilibrium position. The extension $x_{0}$ of the spring when it is in equilibrium is: